Question

he safety director of a large steel mill took samples at random from company records of minor work-related accidents and classified them according to the time the accident took place.

Number of | Number of | |||||||

Time | Accidents | Time | Accidents | |||||

8 up to 9 a.m. | 10 | 1 up to 2 p.m. | 6 | |||||

9 up to 10 a.m. | 6 | 2 up to 3 p.m. | 8 | |||||

10 up to 11 a.m. | 6 | 3 up to 4 p.m. | 7 | |||||

11 up to 12 p.m. | 16 | 4 up to 5 p.m. | 20 | |||||

Using the goodness-of-fit test and the 0.01 level of significance, determine whether the accidents are evenly distributed throughout the day.

*H*_{0}: The accidents are evenly distributed
throughout the day.

*H*_{1}: The accidents are not evenly distributed
throughout the day.

a) State the decision rule, using the 0.01 significance level.

b) Compute the value of chi-square.

c)What is your decision regarding *H*_{0}?

Answer #1

A)The significance level for a given hypothesis test is a value for
which a P-value less than or equal to is considered statistically
significant. If the p value is 0.01 is considered significant or
insignificant for confidence interval of 0.99.

B)

observed frequencies of accidents (fo)=10,6,6,16,6,8,7,20

Total of accidents are: 10+6+6+19+6+8+7+20=79

Average = 79/8

expected frequencies (fe)= 79/8,79/8,79/8,/79/8,79/8,79/8,79/8,79/8

H0: Accidents are evenly distributed throughout the day

H1: Accidents are not evenly distributed throughout the day

chi-square test -statistic =sum(fo-fe)^2/fe = 20.09

Critical value = chi-inv(0.01,7)= 18.475

C)

Since the test statistic does fall inside the rejection region, we
do reject H0.

Using a 0.01 level of significance there is sufficient evidence to
conclude that

the accidents are not evenly distributed throughout the day.

Perform the following tests answering each part. Assume random
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when defects exceed 3%. In a random sample of 85 items, the defect
rate is 5.9% but the manager claims that this is only a sample
fluctuation and production is not really out of control. At the
0.01 level of significance, test the manager's
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